The citing and using of correct version of mathematical equations are of great importance in the writing of a scientific paper. This paper presents the possible errors related to Dubinin-Radushkevich Equation in an article by Igwe and Abia (2007) which was published in Electronic Journal of Biotechnology, 10(4); 536-548.

The Micropore Volume Filling Theory (TVFM) was postulated by Dubinin-Radushkevich for adsorption from gas phase. This equation is based on the Polanyi’s potential theory of the adsorption. Detailed explanation of equations and references related to these theories (Polanyi and Dubinin-Radushkevich) can be found from fundamental text books and some papers written on adsorption and porosity (Gregg and Sing, 1967; Hobson, 1969; Dabrowski, 2001). The theory of Dubinin-Radushkevich is applied to adsorption data to find out adsorption mechanism. The theory also gives some parameters such as adsorption capacity and adsorption energy. 

In the following is one of the commonly used version of the equation in adsorption studies from aqueous solution (Fu et al. 2008);

 (1)

where and are the sorbed amounts at equilibrium and saturation, respectively.   is a constant related to sorption free energy.

Thus, linear form of equation (1) is given as:

  (2)

On the other hand, when the literature is taken into consideration, below versions can also be found as follows:

  (3)

 (4)

In the equations (2-4), e is known as Polanyi potential and it is expressed as follows:

    (5)

where is equilibrium concentration of solute and R the gas constant (J/mol K), T the absolute temperature.

In equation 2-4;  and B are defined as a constant related to adsorption energy. Actually, all of these three symbols present the same constant; however, these symbols change as to how the authors use them. This value ( and B; B hereafter) is found from the slope of the plot between and .

Possible errors in the paper of Igwe and Abia (2007)

When the subtitle of Dubinin-Radushkevich isotherm of the paper reported by Igwe and Abia (2007) is examined, it appears that although the equation [Eq. (4) of Igwe and Abia (2007)] is correct, its linear form [Eq. (5) of Igwe and Abia (2007)] is not correct:

    [Eq. (4) of Igwe and Abia (2007)]

      [Eq. (5) of Igwe and Abia (2007)]

Correct version of the equation [Eq. (5) of Igwe and Abia (2007)] should have been written as follows:

  (6)  or

(7)

Because of the error in the equation [Eq. (5) of Igwe and Abia (2007)], the authors have drawn the plot of lnq_e versus e instead of lnq_e versus e². Therefore, the calculations related to Dubinin-Radushkevich Equation in the paper are not correct and the authors should re-calculate their values by using general accepted and correct version of Dubinin-Radushkevich Equation (Eq. (6) and (7) of this paper). Specifically, the authors should re-draw the Figures 8 and 9, and, then, they should re-calculate the Dubinin-Radushkevich parameters in Table 2. The units of Dubinin-Radushkevich parameters should also be given in Table 2 by the authors.

It is obvious that this error is caused by wrong citation. Igwe and Abia (2007) cited Horsfall et al. (2004)’s paper for Dubinin-Radushkevich Equation. When the Horsfall et al. (2004)’s paper is examined, their explanation related to linear form of Dubinin-Radushkevich Equation is also not correct:

    [Eq. (6) of Horsfall et al (2004)]

      [Eq. (7) of Horsfall et al (2004)]

It is very interesting to note that although Horsfall et al. (2004) made a mistake in writing of Dubinin-Raduskevich Equation, their figure (Figure 6 in the paper of Horsfall et al (2004)) seems true inasmuch as they have a plot of lnq_e versus e² in their paper. However, they should also re-check their data for accuracy.

Horsfall et al. (2004) cited Hasany and Chaudhary (1996) for Dubinin-Radushkevich equation. When Hasany and Chaudhary (1996)’s paper is examined, it is obvious that they correctly expressed the Dubinin-Radushkevich Equation as in the following:

[Eq. (6) of Hasany and Chaudhary (1996)]

A possible mistake by writing of a mathematical equation, as shown in the above, may cause further mistakes in other papers like the chain reactions of polymers. Therefore, the citation is of great importance in writing a scientific paper to a scientific journal. The scientists should cite the correct and original paper when they aim to use a mathematical equation in any field of science or as Fu et al. (2008) mentioned, when the secondary references are used, the equations should be checked -carefully- whether there are any mistakes in their sources. Otherwise, it may cause serious errors in the scientific paper as shown in the present study.

DABROWSKI, A. Adsorption-from theory to practice. Advances in Colloid and Interface Science, 2001, vol. 93, p. 135-224.

FU, L.; WANG, J.; LU, H.; SU, Y. and REN, A. Comment on “The removal of phenolic compounds from aqueous solutions by organophilic bentonite”. Journal of Hazardous Materials, 2008, vol. 151, p. 851-854.

GREGG, S.J. and SING, K.S.W. Adsorption, Surface Area and Porosity, Academic Press London and New York, 1967, p. 195-223.

HASANY, S.M. and CHAUDHARY, M.H. Sorption Potential of Haro River Sand for the Removal of Antimony from Acidic Aqueous Solution. Applied Radiation and Isotopes. 1996, vol. 47, p. 467-471.

HOBSON, J.P. Physical adsorption isotherms extending from ultrahigh vacuum to vapor pressure. Journal of Physical Chemistry, 1969, vol. 73, p. 2720-2727.

HORSFALL, M. Jnr.; SPIFF, A.I. and ABIA, A.A. Studies on the influence of mercaptoacetic acid (MAA) modification of cassava (manihot sculenta cranz) waste biomass on the adsorption of Cu²⁺ and Cd²⁺ from aqueous solution. Bulletin of the Korean Chemical Society, 2004, vol. 25, no. 7, p. 969-976.

IGWE, Jude C. and ABIA, Augustin A. Equilibrium sorption isotherm studies of Cd(II), Pb(II) and Zn(II) ions detoxification from waste water using unmodified and EDTA-modified maize husk. Electronic Journal of Biotechnology [online]. 15 October 2007, vol. 10, no. 4. Available from Internet: http://www.ejbiotechnology.info/content/vol10/issue4/full/15/index.html. ISSN 0717-3458.